How to determine failure on Mohrs Circle

[EzaMoo]

I have already drawn the circle and am happy and confident with it, but the question asks me to determine if failure has occurred and I am unsure of how to tell, I guess I don't know how to read the circle and interpret what it means.

Can anyone describe to me how you tell if failure has occurred on a mohrs circle.

 

[nvn]

EzaMoo: I assume this is ductile material. You could obtain the maximum and minimum principal stress from your Mohr circle. Then compute von Mises stress, sigma_vm, using sigma1 and sigma3. Then compute the stress level w.r.t. yielding, Ry = FSy*sigma_vm/Sty, where FSy = yield factor of safety, and Sty = material tensile yield strength. If Ry ≤ 100 %, the analysis indicates the component is adequate. If Ry > 100 %, the analysis indicates failure.

For design, FSy > 1.0. For failure analysis only, not design, FSy = 1.0.

Keep in mind, the above failure theory (von Mises theory) applies only to isotropic, ductile materials, such as isotropic, ductile metals. Other material types require different failure theories. You must use a failure theory applicable to your material type.